Translate Z Location of object for every frame?
There are a few ways to do this, but essentially you want to parent a camera to the path of the old camera. The easiest way to do this is to:


duplicate the camera SHIFT+D
remove the keyframes on the second camera
parent the second camera to the first camera CTRL+P
change the Transform widget orientation to Local
move the second camera back on the local Z axis
it will still move and pivot with the original camera's orientation.
Select the second Camera and click Set Active Object as Camera CTRL+NUMPAD 0
you can also optionally hide the first camera via the outliner if you find it distracting